0.00/0.13 YES 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 (VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S) 0.00/0.13 (RULES 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ) 0.00/0.13 (STRATEGY INNERMOST) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 Dependency Pairs Processor: 0.00/0.13 -> Pairs: 0.00/0.13 2ND(mark(X:S)) -> 2ND(X:S) 0.00/0.13 2ND(ok(X:S)) -> 2ND(X:S) 0.00/0.13 ACTIVE(2nd(cons(X:S,X1:S))) -> 2ND(cons1(X:S,X1:S)) 0.00/0.13 ACTIVE(2nd(cons(X:S,X1:S))) -> CONS1(X:S,X1:S) 0.00/0.13 ACTIVE(2nd(X:S)) -> 2ND(active(X:S)) 0.00/0.13 ACTIVE(2nd(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> CONS1(active(X1:S),X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> CONS1(X1:S,active(X2:S)) 0.00/0.13 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 0.00/0.13 ACTIVE(from(X:S)) -> FROM(active(X:S)) 0.00/0.13 ACTIVE(from(X:S)) -> FROM(s(X:S)) 0.00/0.13 ACTIVE(from(X:S)) -> S(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> S(active(X:S)) 0.00/0.13 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.13 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.13 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(ok(X1:S),ok(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.13 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.13 PROPER(2nd(X:S)) -> 2ND(proper(X:S)) 0.00/0.13 PROPER(2nd(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> CONS(proper(X1:S),proper(X2:S)) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> CONS1(proper(X1:S),proper(X2:S)) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(from(X:S)) -> FROM(proper(X:S)) 0.00/0.13 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> S(proper(X:S)) 0.00/0.13 S(mark(X:S)) -> S(X:S) 0.00/0.13 S(ok(X:S)) -> S(X:S) 0.00/0.13 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.13 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.13 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.13 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 2ND(mark(X:S)) -> 2ND(X:S) 0.00/0.13 2ND(ok(X:S)) -> 2ND(X:S) 0.00/0.13 ACTIVE(2nd(cons(X:S,X1:S))) -> 2ND(cons1(X:S,X1:S)) 0.00/0.13 ACTIVE(2nd(cons(X:S,X1:S))) -> CONS1(X:S,X1:S) 0.00/0.13 ACTIVE(2nd(X:S)) -> 2ND(active(X:S)) 0.00/0.13 ACTIVE(2nd(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> CONS1(active(X1:S),X2:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> CONS1(X1:S,active(X2:S)) 0.00/0.13 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 0.00/0.13 ACTIVE(from(X:S)) -> FROM(active(X:S)) 0.00/0.13 ACTIVE(from(X:S)) -> FROM(s(X:S)) 0.00/0.13 ACTIVE(from(X:S)) -> S(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> S(active(X:S)) 0.00/0.13 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.13 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.13 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(ok(X1:S),ok(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.13 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.13 PROPER(2nd(X:S)) -> 2ND(proper(X:S)) 0.00/0.13 PROPER(2nd(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> CONS(proper(X1:S),proper(X2:S)) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> CONS1(proper(X1:S),proper(X2:S)) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(from(X:S)) -> FROM(proper(X:S)) 0.00/0.13 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> S(proper(X:S)) 0.00/0.13 S(mark(X:S)) -> S(X:S) 0.00/0.13 S(ok(X:S)) -> S(X:S) 0.00/0.13 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.13 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.13 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.13 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 S(mark(X:S)) -> S(X:S) 0.00/0.13 S(ok(X:S)) -> S(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.13 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(ok(X1:S),ok(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.13 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 2ND(mark(X:S)) -> 2ND(X:S) 0.00/0.13 2ND(ok(X:S)) -> 2ND(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 ACTIVE(2nd(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.13 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 PROPER(2nd(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.13 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 0.00/0.13 0.00/0.13 The problem is decomposed in 8 subproblems. 0.00/0.13 0.00/0.13 Problem 1.1: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 S(mark(X:S)) -> S(X:S) 0.00/0.13 S(ok(X:S)) -> S(X:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(S) = 1 0.00/0.13 0.00/0.13 Problem 1.1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.2: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.13 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(FROM) = 1 0.00/0.13 0.00/0.13 Problem 1.2: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.3: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(ok(X1:S),ok(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(CONS1) = 1 0.00/0.13 0.00/0.13 Problem 1.3: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 0.00/0.13 Problem 1.3: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(CONS1) = 2 0.00/0.13 0.00/0.13 Problem 1.3: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.4: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.13 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(CONS) = 1 0.00/0.13 0.00/0.13 Problem 1.4: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.5: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 2ND(mark(X:S)) -> 2ND(X:S) 0.00/0.13 2ND(ok(X:S)) -> 2ND(X:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(2ND) = 1 0.00/0.13 0.00/0.13 Problem 1.5: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.6: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 ACTIVE(2nd(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.13 ACTIVE(cons1(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.13 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.13 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(ACTIVE) = 1 0.00/0.13 0.00/0.13 Problem 1.6: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.7: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 PROPER(2nd(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.13 PROPER(cons1(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.13 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.13 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(PROPER) = 1 0.00/0.13 0.00/0.13 Problem 1.7: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 0.00/0.13 Problem 1.8: 0.00/0.13 0.00/0.13 Reduction Pairs Processor: 0.00/0.13 -> Pairs: 0.00/0.13 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.13 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.13 top(ok(X:S)) -> top(active(X:S)) 0.00/0.13 -> Usable rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.13 active(s(X:S)) -> s(active(X:S)) 0.00/0.13 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.13 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.13 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.13 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.13 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.13 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.13 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.13 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.13 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.13 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.13 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.13 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.13 ->Interpretation type: 0.00/0.13 Linear 0.00/0.13 ->Coefficients: 0.00/0.13 Natural Numbers 0.00/0.13 ->Dimension: 0.00/0.13 1 0.00/0.13 ->Bound: 0.00/0.13 2 0.00/0.13 ->Interpretation: 0.00/0.13 0.00/0.13 [2nd](X) = 2.X + 2 0.00/0.13 [active](X) = 2.X + 2 0.00/0.13 [cons](X1,X2) = 2.X1 + X2 + 2 0.00/0.13 [cons1](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.13 [from](X) = 2.X + 2 0.00/0.13 [proper](X) = X 0.00/0.13 [s](X) = X 0.00/0.13 [top](X) = 0 0.00/0.13 [fSNonEmpty] = 0 0.00/0.13 [mark](X) = X + 2 0.00/0.13 [ok](X) = 2.X + 2 0.00/0.13 [2ND](X) = 0 0.00/0.13 [ACTIVE](X) = 0 0.00/0.13 [CONS](X1,X2) = 0 0.00/0.13 [CONS1](X1,X2) = 0 0.00/0.13 [FROM](X) = 0 0.00/0.13 [PROPER](X) = 0 0.00/0.13 [S](X) = 0 0.00/0.13 [TOP](X) = 2.X 0.00/0.13 0.00/0.13 Problem 1.8: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.13 -> Rules: 0.00/0.13 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.13 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.13 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.13 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.13 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.13 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.13 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.13 active(from(X:S)) -> from(active(X:S)) 0.00/0.13 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.14 active(s(X:S)) -> s(active(X:S)) 0.00/0.14 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.14 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.14 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.14 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.14 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.14 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.14 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.14 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.14 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.14 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.14 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.14 top(ok(X:S)) -> top(active(X:S)) 0.00/0.14 ->Strongly Connected Components: 0.00/0.14 ->->Cycle: 0.00/0.14 ->->-> Pairs: 0.00/0.14 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.14 ->->-> Rules: 0.00/0.14 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.14 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.14 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.14 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.14 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.14 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.14 active(from(X:S)) -> from(active(X:S)) 0.00/0.14 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.14 active(s(X:S)) -> s(active(X:S)) 0.00/0.14 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.14 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.14 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.14 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.14 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.14 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.14 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.14 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.14 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.14 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.14 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.14 top(ok(X:S)) -> top(active(X:S)) 0.00/0.14 0.00/0.14 Problem 1.8: 0.00/0.14 0.00/0.14 Reduction Pairs Processor: 0.00/0.14 -> Pairs: 0.00/0.14 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.14 -> Rules: 0.00/0.14 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.14 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.14 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.14 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.14 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.14 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.14 active(from(X:S)) -> from(active(X:S)) 0.00/0.14 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.14 active(s(X:S)) -> s(active(X:S)) 0.00/0.14 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.14 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.14 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.14 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.14 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.14 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.14 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.14 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.14 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.14 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.14 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.14 top(ok(X:S)) -> top(active(X:S)) 0.00/0.14 -> Usable rules: 0.00/0.14 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.14 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.14 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.14 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.14 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.14 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.14 active(from(X:S)) -> from(active(X:S)) 0.00/0.14 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.14 active(s(X:S)) -> s(active(X:S)) 0.00/0.14 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.14 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.14 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.14 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.14 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.14 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.14 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.14 ->Interpretation type: 0.00/0.14 Linear 0.00/0.14 ->Coefficients: 0.00/0.14 Natural Numbers 0.00/0.14 ->Dimension: 0.00/0.14 1 0.00/0.14 ->Bound: 0.00/0.14 2 0.00/0.14 ->Interpretation: 0.00/0.14 0.00/0.14 [2nd](X) = 2.X + 2 0.00/0.14 [active](X) = 2.X + 1 0.00/0.14 [cons](X1,X2) = X1 + X2 + 2 0.00/0.14 [cons1](X1,X2) = X1 + 2.X2 + 2 0.00/0.14 [from](X) = 2.X + 2 0.00/0.14 [proper](X) = 0 0.00/0.14 [s](X) = X 0.00/0.14 [top](X) = 0 0.00/0.14 [fSNonEmpty] = 0 0.00/0.14 [mark](X) = X + 1 0.00/0.14 [ok](X) = 2.X + 2 0.00/0.14 [2ND](X) = 0 0.00/0.14 [ACTIVE](X) = 0 0.00/0.14 [CONS](X1,X2) = 0 0.00/0.14 [CONS1](X1,X2) = 0 0.00/0.14 [FROM](X) = 0 0.00/0.14 [PROPER](X) = 0 0.00/0.14 [S](X) = 0 0.00/0.14 [TOP](X) = X 0.00/0.14 0.00/0.14 Problem 1.8: 0.00/0.14 0.00/0.14 SCC Processor: 0.00/0.14 -> Pairs: 0.00/0.14 Empty 0.00/0.14 -> Rules: 0.00/0.14 2nd(mark(X:S)) -> mark(2nd(X:S)) 0.00/0.14 2nd(ok(X:S)) -> ok(2nd(X:S)) 0.00/0.14 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 0.00/0.14 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 0.00/0.14 active(2nd(X:S)) -> 2nd(active(X:S)) 0.00/0.14 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(active(X1:S),X2:S) 0.00/0.14 active(cons1(X1:S,X2:S)) -> cons1(X1:S,active(X2:S)) 0.00/0.14 active(from(X:S)) -> from(active(X:S)) 0.00/0.14 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.14 active(s(X:S)) -> s(active(X:S)) 0.00/0.14 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.14 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.14 cons1(mark(X1:S),X2:S) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 cons1(ok(X1:S),ok(X2:S)) -> ok(cons1(X1:S,X2:S)) 0.00/0.14 cons1(X1:S,mark(X2:S)) -> mark(cons1(X1:S,X2:S)) 0.00/0.14 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.14 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.14 proper(2nd(X:S)) -> 2nd(proper(X:S)) 0.00/0.14 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(cons1(X1:S,X2:S)) -> cons1(proper(X1:S),proper(X2:S)) 0.00/0.14 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.14 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.14 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.14 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.14 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.14 top(ok(X:S)) -> top(active(X:S)) 0.00/0.14 ->Strongly Connected Components: 0.00/0.14 There is no strongly connected component 0.00/0.14 0.00/0.14 The problem is finite. 0.00/0.14 EOF